1. Field of the Invention
The present invention relates to digital image processing and, more particularly, to techniques for sharpening digital images.
2. Related Art
The above-referenced patent entitled “Thermal Imaging System” discloses a printing medium having multiple color-forming layers. Referring to FIG. 1, a schematic diagram is shown of the structure of one embodiment of the media 100 disclosed in the above-referenced patent application. Two of the colorants, yellow and magenta (which for purposes of illustration are shown as one layer but which typically are present in separate layers) 102a, are in close proximity to the top of the media 100, and the third colorant, cyan 102c, is separated from them by a relatively thick base 102b of about 125 μm. Note that the layers 102a-d are not drawn to scale in FIG. 1. Rather, the base layer 102b is much thicker relative to the remaining layers 102a and 102c-d than illustrated in FIG. 1. A TiO2 layer 102d at the bottom of the media 100 provides a white background for an image printed on the media 100. All of the layers 102a-d in the media 100 have essentially the same index of refraction, and the TiO2 layer 102d can be modeled as a diffuse Lambertian reflector.
Referring to FIG. 9, a graph 900 is shown which illustrates the sharpness quality factor (SQF) of edges printed on the media 100 (axis 902b) as a function of mean edge density (axis 902a). As is well-known to those having ordinary skill in the art, SQF is a measure of perceived sharpness. Curve 904a is a plot of mean edge density vs. SQF for a prior art media, such as the media 100 shown in FIG. 1. It can be seen from plot 904a that SQF is a strong function of mean edge density, and that the printed edges lose sharpness as the density decreases. In other words, more blurring occurs at lower densities than at higher densities.
Returning to FIG. 1, this phenomenon may be understood by tracing a path 104 that light takes through the media 100. Upon entry of light into layer 102a of the media 100, a ray of light follows a straight path (based on the assumption that all of the layers 102a-d have the same index of refraction) until it hits the TiO2 layer 102d. The TiO2 layer 102d scatters the incident light, which reemerges from the TiO2 layer 102d at a random angle following the cosine law of a Lambertian reflector. The reflected light from the TiO2 layer 102d follows a straight path back to the surface of the media 100 (through layers 102c, 102b, and 102a).
If the angle of incidence of this reflected light on the media/air interface is large, it will suffer a total internal reflection back into the media 100, as shown in FIG. 1. The process just described will repeat until the ray of light is reflected by the TiO2 layer 102d at a small enough angle such that it does not suffer total internal reflection at the interface of the media 100 and the air 106, and thereby escapes out of the media 100 into the air 106.
Given the large thickness of the base layer 102b, these multiple reflections within the media 100 cause the light to travel a substantial distance laterally (the distance between points 108a and 108b in FIG. 1), resulting in a loss of edge sharpness. The perceived density at any point is obtained by averaging the intensity of rays that have traversed all possible paths through the media 100. This averaging in the linear intensity domain makes the loss in sharpness a function of print density. An edge printed at low density, therefore, is less sharp than an equivalent edge printed at high density.
What is needed, therefore, are techniques for counteracting the effect of such density-dependent blurring to sharpen printed digital images.